let-mathcalb-be-the-basis-of-mathbbp_3-consisting-of-the-hermite-polynomials-in-exercise-21-and-let-

Name: let mathcalb be the basis of mathbbp_3 consisting of the hermite polynomials in exercise 21 and let
Uploaded: 2019-08-08
Duration: 3 min 17 s
Channel: Numerade
Description: Let $\mathcal{B}$ be the basis of $\mathbb{P}_{3}$ consisting of the Hermite polynomials in Exercise $21,$ and let $\mathbf{p}(t)=7-12 t-8 t^{2}+12 t^{3}$ . Find the coordinate vector of $\mathbf{p}$ relative to $\mathcal{B}$ .

Question

Let $\mathcal{B}$ be the basis of $\mathbb{P}_{3}$ consisting of the Hermite polynomials in Exercise $21,$ and let $\mathbf{p}(t)=7-12 t-8 t^{2}+12 t^{3}$ . Find the coordinate vector of $\mathbf{p}$ relative to $\mathcal{B}$ .

Runpeng Li · Accepted Answer

work. Given the faces, that is, um, one one minus t. And to minus 40 us t squared. Yeah. So we have these three a nominal size. Our faces. So we honored to Right down. He up t in terms off. Coordinated back. Factor off P lifted two spaces. First down, Petey is seven miners on a safety plus re t squared. Get less. Dean owed one as p one and one minus TSP too. And do you mind us? 40 plus t squared as p three. So in order to get three t squared, the only the only way to get people can t squared is too is by using the p three. So at least we have to times p three by three. That way we can get three t squared minus well, t, that&#x27;s sick. Only in this way we can get pretty squared. Otherwise, we don&#x27;t have t squared in p to m p one. So And you too. We need to combine Pete even p three to get connective and activate e. And we What we have for Peter is negative t and we&#x27;ve already had we Robert He already had a negative 12 so the only thing we need to do is two times you to buy electric port so that he so that this this, uh, this is equal to negative for last 40 or teeth. Okay. So that our, uh, Osama off three p three milers, four p two will be well, give us negative 80. So, in terms off and then ask in terms off a constant term, we have one. But previous previous stabs our already give us, uh, to because six minus four would be too s o. The only thing we need to add is fight so that to minus to plus five will be seven, which is here. So our final answer will be first three p three minus 42 plus p one. Well, five, if you want. All right, So this is our by no answer.

Doruk Isik · Answer

Yeah, in this trouble were given a set up. So we&#x27;ll start solution by writing the organ directors for each polynomial. So for people in the quarter, Inspector Ho. But like this 101 said, the 1st 1 is the question. But these year old 2nd 1 is to one of you two. So using this Pete, too apartment that too perfect. You could be rich. Zero. What being? And for P three, that could be, um, that would be one one negative three. So then the augmented matrix phoned my bees. Corn factors would be 101 01 negative three and 11 Negative three. Now let&#x27;s write this over mental midgets in traditional echo form. And that is he could do warn. 00010001 is you can see. We have three columns and each column has a few bits elements. So three columns, three events elements at each column. So it means that these vectors Spector&#x27;s spend our fee. It means that the given Colonials no meals spin he two. Now in part, we were given 1/4 collector for a loan Jew, and that is next to 112 And whereas to find this bologna to using this So we know that cube of native one times people plus one p two plus thio three So Dunn will be negative one times ones You&#x27;re one plus one times zero wounding three waas Two times One wonder three And we find this to be one the next 10. And using this, uh, using the information that these numbers represent corruption tease. We can ride the roller milk you is one plus B t minus 10 t spring.

Doruk Isik · Answer

in this problem, we&#x27;re given a set to be, which is a, uh, basis. And we know the full meals that form this base. So we have people are p two mp three in this problem where has to find the coordinate vector that we need to get this balloon GOP off too. So let&#x27;s assume not be coordinating Director. The cell performs. He wants Regency three. So what we know is this you know that c one people plus C to pee too. Plus e t p p should give us given p below me. So we have C one times one minus two squared plus C two times t minus. He&#x27;s very waas. See three times to minus two t plus t spread is a good three plus t minus 60 spread. So we have three unknowns. He wants you to nc three, but we have three new creation, so we have C one less to see. Three busy bee c one plus C 21 c 36 and we have C two minus two City is one. So using this we find see one to be seven you don&#x27;t see too to be negative three and CP to be negative too. Said so it on the coordinates back to that we&#x27;re looking for is seven negative beat and negative too.

Runpeng Li · Answer

first we have the Colleen Ami o Space and we first have the basis that is B, which is one minus three t squared, two plus T minus five. He&#x27;s square and one plus two tea. Okay, so the standard days, that&#x27;s just a key one. This one you do is two. Three. Is he squared? So if we transform those constant and call your patient and two squared by by a P want Peter MP three So we have basis be is you want minus three the three. Two p one us. You do minus why p three And he won t o p. Two. So that gives, uh, change. Accorded a matrix from E to see to see to be first. 10 negative. Three and 2165 and 120 It&#x27;s so here&#x27;s dollar matric. So the next thing we need to write t squared as a wiener combination, not the point. Normalcy B. So that is too. Find a p from E to see times record be e and record UFC and work. Even pfc to is the victor 001 and we will solve this system. 121 There were 12 and the three negative. Five and zero and 001 Here&#x27;s the system we need to solve. So we apply the gushing in the nation two. Why don&#x27;t we? I&#x27;ll just write the result here. That is 100 They&#x27;re all one deal 001 and have three negative to one. So that gives, um, Specter record. PB is three negative too. And what? So our we need a combination is that is three times the first in your question one minus three T squared, minus two times a second question two plus T minus five. T squared to us. T minus five teeth were or we had we say t squared. Where you either We can see three and plus one times off one of us to tea, and we can&#x27;t even check. We have, uh, three minus two. Oh, wait. Um, yeah, we have three. Why is two times two is negative for and plus one. So that&#x27;s countenance with zero. And we have that give 60 squared and and positive 10 t squared and has tools when that years. And yeah, we have, uh So then will leave us a T squared and we have to t cancel two by two t like duty here. So that is exactly two D. Oh, Sorry. Uh, second U T squared.

Arsalan Afkhami · Answer

they flew me out. We have is a zero plus a one X plus a two x. We need to find the victor. That&#x27;s to be even, or the basis, which has three elements one plus x x x minus one Andi one plus two Expert, too Victor Miller before has the From I c one. C two c three to obtain it. We quite the front side. Just you want for it First element setem by second C three by body said so here we re righted a C one plus c one X plus C two, uh, x two. I&#x27;m just multiplying everything minus C two x plus C three bus to he three x or two and the finest Soon our powers off X here it&#x27;s too. And you have, uh, ex then so many Carver. So if we write it again, you will have a system of equations. That is, this has three equations. One first one. These C one plus C three is a close to, uh hey zero as against you here and C three plus C one physicals to his ear. I don&#x27;t seem like for the rest. We&#x27;ll have C one when you see to this close to a gun on C two plus two c three, close to a to then we can write the augmented month metrics cursed by me to these sent if equations the cheese one year show you here is 10 Foresee 21 for C three and a close to a zero. So 10 one most a zero one. Anything you want, Geo. You one true. A one. I hate you. So you reduce it to Rochelle on for by using ghosts and elimination. So we have Ah zero Here. Here. Then we get the reduce for as one geo one 01 200 one You can see here. Um they said zero NGO. So one side off metrics zero. And then here you have a zero a to negative aids you plus a one plus a to. And then you have another system equations, in fact. Ah, this against sold Bite back substitution. So if I write it here Newsome precious is have see one plus C three post a one a a zero and see two plus two c three Those two a to then see three easy cause too Ezio bus a one plus a two. But you can do here is to replace C three to get C two then and also replace C three to get C one. When you&#x27;re done replacing gets the director we&#x27;re looking for, which will be P of X relative to be because to to a zero minus a one, I say to to a zero nice to a bon our state to zero plus a one plus a two. And this is the picture for this problem.

Problem

Let $\mathcal{B}$ be the basis of $\mathbb{P}_{2}…

Problem 23 Easy Difficulty

Let $\mathcal{B}$ be the basis of $\mathbb{P}_{3}$ consisting of the Hermite polynomials in Exercise $21,$ and let $\mathbf{p}(t)=7-12 t-8 t^{2}+12 t^{3}$ . Find the coordinate vector of $\mathbf{p}$ relative to $\mathcal{B}$ .

Answer

$[\vec{P}]_{B}=\left[\begin{array}{c}{3} \\ {3} \\ {-2} \\ {3 / 2}\end{array}\right]$

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

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$[\vec{P}]_{B}=\left[\begin{array}{c}{3} \\ {3} \\ {-2} \\ {3 / 2}\end{array}\right]$

Linear Algebra and Its Applications

Catherine R.

Heather Z.

Kayleah T.

Caleb E.

Vectors Intro

Vector Basics - Example 1

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Catherine R.

Heather Z.

Kayleah T.

Caleb E.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications